William is 24 years older than Kevin. For the last 3 years, William and Kevin have been going to the same school. Thirteen years ago, William was 4 times as old as Kevin. How old is William now?
Explanation: We can use the given information to write down two equations that describe the ages of William and Kevin. Let William's current age be $w$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $w = k + 24$ Thirteen years ago, William was $w - 13$ years old, and Kevin was $k - 13$ years old. The information in the second sentence can be expressed in the following equation: $w - 13 = 4(k - 13)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to solve our first equation for $k$ and substitute it into our second equation. Solving our first equation for $k$ , we get: $k = w - 24$ . Substituting this into our second equation, we get the equation: $w - 13 = 4($ $(w - 24)$ $ -$ $ 13)$ which combines the information about $w$ from both of our original equations. Simplifying the right side of this equation, we get: $w - 13 = 4w - 148$ Solving for $w$ , we get: $3 w = 135$ $w = 45$.